Isometric Axes: The lines AB, AD and AE meeting at a point A and making an angle of 120 o with each other are termed isometric axes

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1 ISOMTRI PROJTION When a solid is resting in its simple position, the front or top view, taken separately, gives an incomplete idea of the form of the object. When the solid is tilted from its simple position such that its axis is inclined to both H.P and V.P, the front view or the top view or sometimes both, give an air idea of the pictorial form of the object, i.e., all the surfaces are visualized in a single orthographic view. Iso means equal and metric projection means a projection to a reduced measure. n isometric projection is one type of pictorial projection in which the three dimensions of a solid are not only shown in one view, but also their dimension can be scaled from this drawing. R 30 o 45 o G 20 o H 20 o 20 o It is seen that all the edges and faces of the rectangular prism are equally inclined to the plane of all the edges and faces of the cube are equally inclined to the plane of projection. Hence the rectangular faces are seen as similar and equal rhombuses. The three lines, and are meeting at. These edges are mutually perpendicular to each other in the solid. Since all these edges are equally inclined to H.P, they are making and angle of 20 o with each other in the plane of projection; also they are equally foreshortened. This leads us to the problem of selecting an isometric scale. Isometric xes: The lines, and meeting at a point and making an angle of 20 o with each other are termed isometric axes

2 Isometric Lines: The lines parallel to the isometric axes are termed isometric lines. The lines, etc are examples of isometric lines. Non-isometric Lines: The lines which are not parallel to isometric axes are termed non-isometric lines. The is an example. Isometric Planes: The planes representing the faces of the rectangular prism as well as other planes parallel to these planes are termed isometric planes. Isometric scale: Isometric projection is drawn using isometric scale, which converts true lengths into isometric lengths (foreshortened) onstruction of isometric scale: raw a horizontal line. rom draw a line at 45 o to represent actual or true length and another line at 30 o to to measure isometric length. On mark the point 0,, 2 etc to represent actual lengths. rom these points draw verticals to meet at 0,, 2 etc. The length represents the isometric scale length of and so on. Isometric Length = cos 45 o = = cos 30 o = = 2 = = = = Isometric Length = 0.8 ctual Length ctual Length o 2 45 o o Isometric Length

3 ifference between isometric view and isometric projection Isometric View rawn to actual scale When lines are drawn parallel to isometric axes, the true lengths are laid off. Isometric Projection rawn to isometric scale When lines are drawn parallel to isometric axes, the lengths are foreshortened to 0.8 time the actual lengths. ORTHOGRPHI PROJTION ISOMTRI PROJTION ISOMTRI VIW Isometric Plane and Non-isometric Plane: Isometric Planes are marked as and Non-isometric Planes are marked as o 30 o G H 3

4 Problem raw the isometric projection of a rectangular prism of base 50 mm 0 mm and height 75 mm, when it rests with its base on H.P and one its of rectangular faces is parallel to V.P R 75 mm 75 mm 3 Z da RONT VIW cb 50 mm 40 mm 30 o X 45 o Y a b 40 mm d 50 mm c TOP VIW b 30 o 30 o a 30 o 30 o d c 4

5 OX MTHO: The isometric projection of solids like cube, square and rectangular prisms are drawn directly when their edges are parallel to the three isometric axes. The isometric projection of all other types of prisms and cylinders are drawn by enclosing them in a rectangular box. This method is called ox method. XMPL raw an isometric of a Pentagonal prism of base.5 and length 2.5 resting on one of its rectangular faces on H.P.5" 2.5" 30 o 30 o ISOMTRI VIW O RGULR PNTGONL PRISM (Resting on one of its rectangular faces on H.P) 5

6 XMPL 2 raw an isometric of a Hexagonal Prism of base and length 3 resting on one of its rectangular faces on H.P 3" 30 o 30 o ISOMTRI VIW O RGULR HXGONL PRISM (Resting on one of its rectangular faces on H.P) 6

7 XMPL 3 raw an isometric of a Octagonal Prism of base.5 and length 2.5 resting on one of its rectangular faces on H.P G H.5" 2.5" G G H H 30 o 30 o ISOMTRI VIW O N OTGONL PRISM (Resting on one of its rectangular faces on H.P) 7

8 XMPL 4 raw an isometric of a regular Hexagonal Pyramid of base and height 3 resting on one of its hexagonal faces on H.P 3" 30 o 30 o ISOMTRI VIW O RGULR HXGONL PRISM (Resting on one of its hexagonal faces on H.P) 8

9 OUR NTR MTHO: XMPL 5 raw an isometric of a cylinder of base diameter and height 3 lying on H.P rawing Procedure Join P with and which are the mid-points of the opposite sides of the rhombus. Similarly join R with and. With P as centre and P as radius draw an arc. Similarly with R as centre and R as radius draw an arc. The lines P and R intersect at O. With O as centre and O as radius draw an arc. Similarly with O 2 (intersection of R and P) as centre and O 2 as radius draw an arc. Thus complete the ellipse. Refer step -3 in the Offset method and complete the isometric view of the cylinder. S R O O 2 P 30 o Q 30 o ISOMTRI VIW O YLINR (Lying on H.P) 9

10 XMPL 6 raw an isometric of a cylinder of base diameter and height 3 lying on V.P rawing Procedure Join P with and which are the mid-points of the opposite sides of the rhombus. Similarly join R with and. With P as centre and P as radius draw an arc. Similarly with R as centre and R as radius draw an arc. The lines P and R intersect at O. With O as centre and O as radius draw an arc. Similarly with O 2 (intersection of R and P) as centre and O 2 as radius draw an arc. Thus complete the ellipse. Refer step -3 in the Offset method and complete the isometric view of the cylinder. R S O O 2 Q 30 o P 30 o ISOMTRI VIW O YLINR (Lying on V.P) 0

11 O-ORINT OR OST MTHO: XMPL The isometric view of a hexagonal pyramid of side of base 30 mm and height 75 mm, when it is resting on H.P such that an edge of the base is parallel to V.P rawing Procedure raw the top and front views of the hexagonal pyramid. nclose the hexagon in a rectangle PQRS in the top view. raw the isometric vies of the base of the pyramid in the parallogram PQRS. Note that is an isometric line on which O lies. Hence mark O on the isometric line such that O = y. rom O erect a vertical line and mark the apex O such that O O = length of the axis = 75 mm Join O with all the corners of the base of the pyramid and complete the isometric as shown. O 75 mm O O S R R OO OO P Q S O Q O y P 30 mm

12 XMPL 2 raw the isometric projection of a cone of base 40 mm diameter and height 58 mm when it rest with its base on H.P rawing Procedure raw the orthographic projections of the cone. nclose the circle in top view in a square PQRS. raw the isometric vies of the base of the pyramid in the parallogram PQRS. raw the base of the cone as an ellipse by our-centre method. rom and draw line parallel to isometric axes and obtain O (Offset method). rom O draw a line parallel to the third axis. On this line mark O such that O O = height of the cone = 58 mm rom O draw two tangents to the ellipse and complete the isometric projection of the cone. O 58 mm O O R R OO x 40 mm S O Q S O Q x P P 2

13 raw the Top view, ront view, Right view, Left view and ack view for the following isometric view. 3 0" 6" 6" 6" 6" 0" 0" 3 0" 6" 6" 6" 30 o 30 o RONT VIW 3 0" 6" 6" 6" 0" 0" 6" TOP VIW - 6" LT VIW 0" 0" 3

14 ¼" 2¾" 3 " 8 2¾" 2¼" 3" 7 " 8 3 ¾" 3" ¼" 3 5 5/8" 3¾" 2¾" /8" 2¾" RONT VIW LT VIW RONT VIW LT VIW 2 TOP VIW TOP VIW 4

15 4. 2.5" LT VIW RIGHT VIW.5" TOP VIW RONT VIW 5

16 5. RONT VIW TOP VIW LT VIW RIGHT VIW 6

17 6. ½ ½ ½ ½ ½ ½ RONT VIW LT VIW ½ ½ ½ RIGHT VIW TOP VIW 7

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19 @6 = -6 RONT VIW @6 = @0 =2-6 LT VIW 9

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